Type the systems into 'Algebrator' but instead of 'and' put comma:

6m<=-36 and m+24>20 gives solution m<=-6, m>-4 (click here to see the solving)

Since there is no such m, 6m<_-36 and m+24>20 has no solution.

-2m<6 and 3m>24 gives solution m>8 (click here to see the solving)

Thus -2m<6 and 3m>24 has solution.

8m+5>_5 and -4m+6<_-10 gives solution m>0 (click here to see the solving)

Thus 8m+5>_5 and -4m+6<_-10 has solution.

m+9<8 and -2m>_10 gives solution m<-1 (click here to see the solving)

Thus m+9<8 and -2m>_10 has solution.

So the final answer is: out of the given systems of inequalities, 6m<_-36 and m+24>20 has no solution.